\newproblem{lay:4_7_1}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 4.7.1}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Let $B=\{\mathbf{b}_1,\mathbf{b}_2\}$ and $C=\{\mathbf{c}_1,\mathbf{c}_2\}$ be bases for a vector space $V$, and suppose
	$\mathbf{b}_1=6\mathbf{c}_1-2\mathbf{c}_2$ and $\mathbf{b}_2=9\mathbf{c}_1-4\mathbf{c}_2$.
	\begin{enumerate}[a.]
		\item Find the change-of-coordinates matrix from $B$ to $C$.
		\item Find $[\mathbf{x}]_C$ for $\mathbf{x}=-3\mathbf{b}_1+2\mathbf{b}_2$
	\end{enumerate}
}{
  % Solution
	\begin{enumerate}[a.]
		\item The change-of-coordinates matrix is\\
			\begin{center}
				$P_{C\leftarrow B}=\begin{pmatrix}[\mathbf{b}_1]_C & [\mathbf{b}_2]_C\end{pmatrix}=\begin{pmatrix}6 & 9 \\ -2 & -4\end{pmatrix}$
			\end{center}
		\item We note that $[\mathbf{x}]_B=\begin{pmatrix}-3\\2\end{pmatrix}$, then
			\begin{center}
				$[\mathbf{x}]_C=P_{C\leftarrow B}[\mathbf{x}]_B=\begin{pmatrix}6 & 9 \\ -2 & -4\end{pmatrix}\begin{pmatrix}-3\\2\end{pmatrix}=\begin{pmatrix}0\\-2\end{pmatrix}$
			\end{center}
	\end{enumerate}
}
\useproblem{lay:4_7_1}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
